Abstract: This paper discussed a dynamic control problem of a monopolist who invested in the product innovation and goodwill in a market with network externality and adopted the regulated price. Under the monopoly optimum, it is concluded that there exists a unique stable steady state equilibrium, which is a saddle point. When the symbol of the change rate of investment in improving product quality and goodwill investment is the same (opposite), the two kinds of investment are complementary (substitutable). As the fixed strength of network externality increases with other parameters being kept constant, it is very likely that the steady-state investment of the monopolist in product innovation increases with the product quality. The steady-state equilibrium investments of the monopolist are substitutes when there are some slight variations in product quality in the neighborhood of the steady-state equilibrium.

Key words: product innovation, price regulation, network externality, goodwill

摘要： 建立了网络外部性条件下企业产品创新(提高产品质量)与广告投资(提高产品商誉)关系的最优动态控制模型。进一步，本模型中不但考虑了产品价格的管制问题，而且产品价格取决于产品质量。研究结论表明：系统存在唯一的鞍点均衡，并且，当提高产品质量的投资和商誉投资变化率的符号相同（相反）时，两种投资具有互补性（替代性）。此外，当网络外部性的固定强度增大时，系统在均衡状态下的产品创新投资随着产品质量的提高而增加，并且产品质量在稳态状态附近变动时，产品创新投资和商誉投资具有互补性。

关键词: 产品创新, 价格管制, 网络外部性, 商誉